Modernize and simplify AudioState

Update the class to be more in line with the rest of the code, improve
thread safety annotations, naming etc of the internal AudioState
implementation.

* Remove the unused process_thread_checker_.
* Rename thread_checker_ to worker_thread_checker_ to clarify its
  underlying purpose.
* Add thread safety annotations (RTC_GUARDED_BY and RTC_RUN_ON) to
  member variables and helper methods to enforce proper access.
* Replace std::map with flat_map for storing sending streams to
  align with the expected memory footprint.
* Clean up redundant webrtc:: namespace prefixes across the file.
* Mark the audio_device_module() accessor method as const.

Bug: none
Change-Id: Ie97ca8d367bcd12ee790b813ea1f6f2cb1b35ecb
Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/479500
Commit-Queue: Tomas Gunnarsson <tommi@webrtc.org>
Reviewed-by: Jakob Ivarsson‎ <jakobi@webrtc.org>
Cr-Commit-Position: refs/heads/main@{#47919}